(25 points) A ho-airbllon, ntilly empty, is filled at a constant atmospheric pre
ID: 1789737 • Letter: #
Question
(25 points) A ho-airbllon, ntilly empty, is filled at a constant atmospheric pressure of ls fileld with hor ar a120E, and heat conduction through the balloon walls during filling maintain the comtens a cosazt average 80°E. The opening is 25 ft in cross-sectional area. velc is 0.5 ft/ls, what is the mass flow rate of air entering, in lbm/s? bI te bello dimensions a ill in seconds? ions are approximately a sphere of radius 30 feet, how long will it take to c hw tuch boundary work, W, is done to fill the balloon completely, in Btu? d ie the relevant energy balance filling proces ce for this filling process in terms of thermodynamics properties abes (4 Q, W, u, h, m, etc.) How murch heat is conducted through the balloon wall, in Btu, and in what direction, IN or OUT?Explanation / Answer
a. temperature of the hot air being filled Th = 120 F = 322.039 K
pressure at which the baloon is filled, Pi = 14.7 psia = 101352.9 Pa
using ideal gas equation for air
P = rho*RT ( where Rho is density of air and R is gas copnstant of air = 287.058)
so rho = Pi/287.058*Th = 1.0964 kg/m^3
flow inlet area A =25ft^2 = 2.32258 m^2
flow velocity, v = 0.5 ft/s = 0.1524 m/s
hence mass flow rate, r = rho*A*v = 0.3880830509088 kg / s = 0.8555766731896306 lb / s
b. temperature inside ballon, T = 80F = 299.817 K
density inside baloon, rho' = ?
using ideal gas equation
Pi = rho*R*T
hence
rho' = 1.17763 kg/m^3]
radius of baloon, R = 30 ft = 9.144 m
volume of the baloon = 4*pi*R^3/3 = 3202.5599 m^3
hence
time taken for the baloon to fill = t
r*t = rho'*V
t = 1.17763 *3202.5599 / 0.3880830509088 =9718.10185 s = 2.699 hrs
c. work done to fill the baloon = Pi*V = 101352.9*3202.5599 = 324588733.28871 J = 307650.75847185246 BTU
d. heat lost = Q
work done on the baloon = W
change ion internal energy of baloonm = U
from conservation of energy
W = Q + U
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.